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Theorem tncp 21758
 Description: There exist three non colinear points. (Contributed by FL, 3-Aug-2009.)
Hypothesis
Ref Expression
tncp.1
Assertion
Ref Expression
tncp
Distinct variable groups:   ,,,,   ,,,
Allowed substitution hint:   ()

Proof of Theorem tncp
StepHypRef Expression
1 tncp.1 . . . 4
21isplig 21757 . . 3
32ibi 233 . 2
43simp3d 971 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725   wne 2598  wral 2697  wrex 2698  wreu 2699  cuni 4007  cplig 21755 This theorem is referenced by:  lpni  21759 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-reu 2704  df-v 2950  df-uni 4008  df-plig 21756
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